Biography:Manfredo do Carmo

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Short description: Brazilian mathematician
Manfredo do Carmo
Manfredo do Carmo 1979 (headshot, enlarged).jpg
do Carmo in 1979
Born(1928-08-15)15 August 1928
Maceió, Alagoas
Died30 April 2018(2018-04-30) (aged 89)
Rio de Janeiro
Resting placeCemitério de São João Batista
NationalityBrazilian
Alma materUniversity of California, Berkeley
AwardsGuggenheim Fellowship (1965, 1968)
Prêmio Almirante Álavaro Alberto (1984)
Brazil's National Order of Scientific Merit (1995)
TWAS Prize (1987)
AMS Fellow (2012)
Scientific career
FieldsMathematics
InstitutionsInstituto Nacional de Matemática Pura e Aplicada
ThesisThe Cohomology Ring of Certain Kahlerian Manifolds (1963)
Doctoral advisorShiing-Shen Chern
Doctoral studentsCelso Costa
Marcos Dajczer
Keti Tenenblat

Manfredo Perdigão do Carmo (15 August 1928, Maceió – 30 April 2018, Rio de Janeiro) was a Brazil ian mathematician. He spent most of his career at IMPA and is seen as the doyen of differential geometry in Brazil.[1]

Education and career

Do Carmo studied civil engineering at the University of Recife from 1947 to 1951. After working a few years as engineer, he accepted a teaching position at the newly created Institute of Physics and Mathematics at Recife.[2]

On suggestion of Elon Lima, in 1959 he went to Instituto Nacional de Matemática Pura e Aplicada to improve his background[2][3] and in 1960 he moved to the US to pursue a Ph.D. in mathematics at the University of California, Berkeley under the supervision of Shiing-Shen Chern. He defended his thesis, entitled "The Cohomology Ring of Certain Kahlerian Manifolds", in 1963.[4]

After working again at University of Recife and at the University of Brasilia, in 1966 he became professor at Instituto Nacional de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro. From 2003 to his death he was emeritus professor at the same institution.[2]

Do Carmo was a Guggenheim Fellow in 1965 and 1968.[5][6] In 1978 he was invited speaker at the International Congress of Mathematicians held in Helsinki.[7][8][9] In 1991 he obtained a Doctorate honoris causa from Federal University of Alagoas[10][11] and in 2012 from University of Murcia[12][13] and from Federal University of Amazonas.[14][15]

He served as president of the Brazilian Mathematical Society in the term 1971–1973.[16] He was elected a member of the Brazilian Academy of Sciences in 1970,[17] a member of The World Academy of Sciences (TWAS) in 1997[18] and a fellow of the American Mathematical Society In 2013.[19]

Among his awards, he received the Prêmio Almirante Álavaro Alberto from the National Council for Scientific and Technological Development in 1984,[20] the TWAS Prize in Mathematics in 1992,[18][21] the National Order of Scientific Merit in 1995[22] and the Comenda Graciliano Ramos from the municipality of Maceió in 2000.

Do Carmo died on 30 April 2018 at the age of 89.[23][24][25]

Research

Do Carmo's main research interests were Riemannian geometry and the differential geometry of surfaces.[3]

In particular, he worked on rigidity and convexity of isometric immersions,[26][27] stability of hypersurfaces[28][29] and of minimal surfaces,[30][31] topology of manifolds,[32] isoperimetric problems,[33] minimal submanifolds of a sphere,[34][35] and manifolds of constant mean curvature[36][37][38][39] and vanishing scalar curvature.[40]

Do Carmo published more than 100 papers in peer-reviewed journals;[41] in 2012 a selection of his works was published by Springer.[42] He is also known for his textbooks:[43][44] they were translated into many languages and used in courses from universities such as Harvard and Columbia.[45][2]

He supervised 27 PhD students, including Celso Costa, Marcos Dajczer and Keti Tenenblat.[4]

Books

  • Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976 ISBN:9780132125895
  • Riemannian Geometry, Birkhäuser, 1992 ISBN:978-0-8176-3490-2
  • Differential Forms and Applications, Springer Verlag, Universitext, 1994 ISBN:978-3-540-57618-1
  • (with Eduardo Wagner and Augusto Cezar de Oliveira Morgado). Trigonometria – Números Complexos ISBN:8583370168

References

  1. ↑ Gorodski, Claudio; Piccione, Paolo (2021-06-01). "Opening note: An homage to Manfredo P. do Carmo" (in en). São Paulo Journal of Mathematical Sciences 15 (1): 1–2. doi:10.1007/s40863-020-00194-0. ISSN 2316-9028. 
  2. ↑ 2.0 2.1 2.2 2.3 Queiroz, Antonio José Melo de (2020). "O percurso profissional de Manfredo Perdigão do Carmo e a geometria differencial no Brasil" (in pt). Boletim Cearense de Educação e História da Matemática 7 (20): 266–276. doi:10.30938/bocehm.v7i20.2819. ISSN 2447-8504. https://revistas.uece.br/index.php/BOCEHM/article/view/2819. 
  3. ↑ 3.0 3.1 Carmo, Manfredo P. do (2012), do Carmo, Manfredo P.; Tenenblat, Keti, eds., "A Summary of the Scientific Activities" (in en), Manfredo P. do Carmo – Selected Papers (Berlin, Heidelberg: Springer): pp. 1–5, doi:10.1007/978-3-642-25588-5_1, ISBN 978-3-642-25588-5, https://doi.org/10.1007/978-3-642-25588-5_1, retrieved 2022-01-31 
  4. ↑ 4.0 4.1 Manfredo do Carmo at the Mathematics Genealogy Project
  5. ↑ Biography from the Guggenheim Foundation
  6. ↑ "John Simon Guggenheim Foundation | Manfredo Perdigao do Carmo" (in en-US). https://www.gf.org/fellows/all-fellows/manfredo-perdigao-do-carmo/. 
  7. ↑ Lehto, Olii, ed (1980). Proceedings of the International Congress of Mathematician 1978. Helsinki. pp. 401. https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1978.1/ICM1978.1.ocr.pdf. 
  8. ↑ do Carmo, Manfredo P. (1980), "Minimal surfaces: stability and finiteness", Proceedings of the International Congress of Mathematicians (Helsinki, 1978), Acad. Sci. Fennica, Helsinki, pp. 401–405 .
  9. ↑ Carmo, Manfredo P. do (2012), do Carmo, Manfredo P.; Tenenblat, Keti, eds., "Minimal Surfaces: Stability and Finiteness" (in en), Manfredo P. do Carmo – Selected Papers (Berlin, Heidelberg: Springer): pp. 139–143, doi:10.1007/978-3-642-25588-5_12, ISBN 978-3-642-25588-5, https://doi.org/10.1007/978-3-642-25588-5_12, retrieved 2022-02-01 
  10. ↑ "Ufal promove evento internacional na área de Matemática" (in pt-br). https://ufal.br/ufal/noticias/2014/03/ufal-promove-evento-internacional-na-area-de-matematica. 
  11. ↑ "Alagoano referência em geometria diferencial será homenageado em evento" (in pt-br). https://ufal.br/ufal/noticias/2018/6/alagoano-referencia-em-geometria-diferencial-sera-homenageado-em-evento. 
  12. ↑ "Professor Manfredo P. Do Carmo will be awarded the honorary degree Doctor Honoris Causa by the Universidad de Murcia | European Mathematical Society". https://euro-math-soc.eu/news/12/02/28/professor-manfredo-p-do-carmo-will-be-awarded-honorary-degree-doctor-honoris-causa. 
  13. ↑ (in es) Laudatio del Padrino, 2012-05-15, https://tv.um.es/video?id=35671&idioma=es&serie=8281&autoplay, retrieved 2022-02-06 
  14. ↑ "Ata da sessão solene de outorga de titulo Dr. Honoris Causa" (in pt). https://conselhos.ufam.edu.br/images/atas/ata-da-sessao-solene-de-outorga-de-titulo-dr-honoris-causa-18072012-consuni.pdf. 
  15. ↑ "Resolução N° 009/2012" (in pt). https://conselhos.ufam.edu.br/images/deliberacoes/res0092012suni-.pdf. 
  16. ↑ "Diretorias Anteriores – SBM – Sociedade Brasileira de Matemática" (in pt-BR). https://sbm.org.br/diretorias-anteriores/. 
  17. ↑ "Manfredo Perdigão do Carmo – ABC" (in pt-BR). https://www.abc.org.br/membro/manfredo-perdigao-do-carmo/. 
  18. ↑ 18.0 18.1 "do Carmo, Manfredo P." (in en). https://twas.org/directory/do-carmo-manfredo-p. 
  19. ↑ List of Fellows of the American Mathematical Society, retrieved 2015-01-13.
  20. ↑ "CNPq - Prêmio Almirante Álvaro Alberto" (in pt). http://www.premioalvaroalberto.cnpq.br/laureados.html. 
  21. ↑ "Prizes and Awards". The World Academy of Sciences. 2016. http://twas.org/opportunities/prizes-and-awards. 
  22. ↑ "Ordem Nacional do Mérito Científico" (in pt). Instituto Brasileiro de Informação em Ciência e Tecnologia [pt]. 11 August 2023. https://canalciencia.ibict.br/quem-somos2/noticias/item/237-ordem-nacional-do-merito-cientifico. 
  23. ↑ "Matemático Manfredo do Carmo morre aos 89 anos" (in pt). IMPA. https://impa.br/page-noticias/matematico-manfredo-do-carmo-morre-aos-89-anos/. 
  24. ↑ "Decease of Prof. Do Carmo | European Mathematical Society". https://euro-math-soc.eu/news/18/05/2/decease-prof-do-carmo. 
  25. ↑ "News from the AMS" (in en). https://www.ams.org/news?news_id=4325. 
  26. ↑ do Carmo, M. P.; Warner, F. W. (1970). "Rigidity and convexity of hypersurfaces in spheres". Journal of Differential Geometry 4 (2). doi:10.4310/jdg/1214429378. ISSN 0022-040X. 
  27. ↑ doCarmo, Manfredo P.; Lima, Elon (1969-05-01). "Isometric immersions with semi-definite second quadratic forms" (in en). Archiv der Mathematik 20 (2): 173–175. doi:10.1007/BF01899010. ISSN 1420-8938. https://doi.org/10.1007/BF01899010. 
  28. ↑ Barbosa, João Lucas; do Carmo, Manfredo (1984-09-01). "Stability of hypersurfaces with constant mean curvature" (in en). Mathematische Zeitschrift 185 (3): 339–353. doi:10.1007/BF01215045. ISSN 1432-1823. https://doi.org/10.1007/BF01215045. 
  29. ↑ Barbosa, J. Lucas; do Carmo, Manfredo; Eschenburg, Jost (1988-03-01). "Stability of hypersurfaces of constant mean curvature in Riemannian manifolds" (in en). Mathematische Zeitschrift 197 (1): 123–138. doi:10.1007/BF01161634. ISSN 1432-1823. https://doi.org/10.1007/BF01161634. 
  30. ↑ Barbosa, J. L.; Carmo, M. Do (1976). "On the Size of a Stable Minimal Surface in R3". American Journal of Mathematics 98 (2): 515–528. doi:10.2307/2373899. ISSN 0002-9327. https://www.jstor.org/stable/2373899. 
  31. ↑ do Carmo, M.; Peng, C. K. (1979). "Stable complete minimal surfaces in 𝑅³ are planes" (in en). Bulletin of the American Mathematical Society 1 (6): 903–906. doi:10.1090/S0273-0979-1979-14689-5. ISSN 0273-0979. https://www.ams.org/bull/1979-01-06/S0273-0979-1979-14689-5/. 
  32. ↑ do Carmo, Manfredo; Xia, Changyu (2000-02-01). "Ricci curvature and the topology of open manifolds" (in en). Mathematische Annalen 316 (2): 391–400. doi:10.1007/s002080050018. ISSN 1432-1807. https://doi.org/10.1007/s002080050018. 
  33. ↑ Barbosa, João Lucas; Carmo, Manfredo do (1978-10-01). "A proof of a general isoperimetric inequality for surfaces" (in en). Mathematische Zeitschrift 162 (3): 245–261. doi:10.1007/BF01186367. ISSN 1432-1823. https://doi.org/10.1007/BF01186367. 
  34. ↑ Chern, S. S.; do Carmo, M.; Kobayashi, S. (1970), Browder, Felix E., ed., "Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length" (in en), Functional Analysis and Related Fields: Proceedings of a Conference in honor of Professor Marshall Stone, held at the University of Chicago, May 1968 (Berlin, Heidelberg: Springer): pp. 59–75, doi:10.1007/978-3-642-48272-4_2, ISBN 978-3-642-48272-4, https://doi.org/10.1007/978-3-642-48272-4_2, retrieved 2022-02-01 
  35. ↑ Carmo, Manfredo P. Do; Wallach, Nolan R. (1971). "Minimal Immersions of Spheres into Spheres". Annals of Mathematics 93 (1): 43–62. doi:10.2307/1970752. ISSN 0003-486X. https://www.jstor.org/stable/1970752. 
  36. ↑ do Carmo, Manfredo P.; Dajczer, Marcos (1982-01-01). "Helicoidal surfaces with constant mean curvature". Tohoku Mathematical Journal 34 (3). doi:10.2748/tmj/1178229204. ISSN 0040-8735. 
  37. ↑ Carmo, M. Do; Dajczer, M. (1983). "Rotation Hypersurfaces in Spaces of Constant Curvature". Transactions of the American Mathematical Society 277 (2): 685–709. doi:10.2307/1999231. ISSN 0002-9947. https://www.jstor.org/stable/1999231. 
  38. ↑ Alencar, Hilário; do Carmo, Manfredo (1994). "Hypersurfaces with constant mean curvature in spheres" (in en). Proceedings of the American Mathematical Society 120 (4): 1223–1229. doi:10.1090/S0002-9939-1994-1172943-2. ISSN 0002-9939. https://www.ams.org/proc/1994-120-04/S0002-9939-1994-1172943-2/. 
  39. ↑ Bérard, P.; do Carmo, M.; Santos, W. (1998-06-01). "Complete Hypersurfaces with Constant Mean Curvature and Finite Total Curvature" (in en). Annals of Global Analysis and Geometry 16 (3): 273–290. doi:10.1023/A:1006542723958. ISSN 1572-9060. https://doi.org/10.1023/A:1006542723958. 
  40. ↑ Barbosa, J. L. M.; Carmo, M. P. Do (2005-09-01). "On Stability of Cones in Rn+1 with Zero Scalar Curvature" (in en). Annals of Global Analysis and Geometry 28 (2): 107–122. doi:10.1007/s10455-005-0039-5. ISSN 1572-9060. https://doi.org/10.1007/s10455-005-0039-5. 
  41. ↑ "zbMATH Open - the first resource for mathematics". https://zbmath.org/authors/?q=ai:do-carmo.manfredo-perdigao. 
  42. ↑ do Carmo, Manfredo P. (2012). Tenenblat, Keti. ed (in en-gb). Manfredo P. do Carmo – Selected Papers. doi:10.1007/978-3-642-25588-5. ISBN 978-3-642-25587-8. https://doi.org/10.1007/978-3-642-25588-5. 
  43. ↑ do Carmo, Manfredo P. (1994). "Differential Forms and Applications" (in en-gb). Universitext. doi:10.1007/978-3-642-57951-6. ISBN 978-3-540-57618-1. ISSN 0172-5939. https://doi.org/10.1007/978-3-642-57951-6. 
  44. ↑ Carmo, Manfredo Perdigão do (1992). Riemannian geometry. Francis J. Flaherty. Boston: Birkhäuser. ISBN 0-8176-3490-8. OCLC 24667701. https://www.worldcat.org/oclc/24667701. 
  45. ↑ Shozo Motoyama, ed (2004) (in pt). Prelúdio para uma história: ciência e tecnologia no Brasil. EdUSP. p. 358. ISBN 978-85-314-0797-0. https://books.google.com/books?id=z_BNPYRNmyYC&pg=PA358. 



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